Representation theory and ADHM-construction on quaternion symmetric spaces

Abstract

We determine all irreducible homogeneous bundles with anti-selfdual canonical connections on compact quaternion symmetric spaces. To deform the canonical connections, we give a relation between the representation theory and the theory of monads on the twistor space. The moduli spaces are described via the Bott-Borel-Weil Thereom. The Horrocks bundle is also generalized to higher-dimensional projective spaces.